Computation of the eigenvalues of Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method

The purpose in this paper is to compute the eigenvalues of Sturm-Liouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter using the regularized sampling method, an improvement on the method based on Shannon sampling theory, which does not involve any multiple integration and provides higher order estimates of the eigenvalues at a very low cost. A few examples shall be presented to illustrate the power of the method and a comparison made with the the exact eigenvalues obtained as squares of the zeros of the exact characteristic functions.

     

Luminescence kinetic and association equilibria of lanthanide ions in aqueous solutions. II. Determination of the formation constant of Tb acetato complex by means of luminescence lifetime measurement

The association constant K of mono-acetato complex of Tb³⁺ has been determined at normal p and T conditions by measurement of its luminescence lifetime in aqueous solution containing increasing concentrations of acetate. Two experimental arrangements used for the measurement are described.     

Characterization of n-butyl acrylate centered triads in poly(n-butyl acrylate-co-carbon monoxide-co-ethylene) by isotopic labeling and two dimensional NMR

Poly(n-butylacrylate-co-carbon monoxide-co-ethylene) (polyEBC) samples prepared from 13C-labeled monomer, n-butyl acrylate, were characterized using two dimensional (2D) pulsed field gradient (PFG) 750 MHz NMR spectroscopy. To elucidate the complex structure of the terpolymer, 2D-1H/13C-heteronuclear single quantum coherence (HSQC) and heteronuclear multiple bond correlation (HMBC) experiments were conducted by selectively exciting the enhanced resonances in the spectra of two polymer samples, one polymer resulting from synthesis with 1-13C-n-butylacrylate monomer and a second polymer obtained from a synthesis with 2-13C-n-butylacrylate monomer. High-resolution 2D-NMR combined with 13C-labeling of the polymer greatly simplifies the 2D-NMR spectra, selectively enhances the weak peaks from low occurrence B-centered triad structures, and aids in their resonance assignments. In all experiments, the sample temperature was 120 degrees C, to ensure a homogeneous solution and sufficient molecular mobility. Electronic Supplementary Material: Supplementary material (1D 13C NMR spectra of the 13C-labeled and unlabeled polymers) is available in the online version of this article at http://dx.doi.org/100.1007/s00216-003-2402-3.     

Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD

We explicitly determine the global structure of the SL(2, ) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.     

Trennung von Spurenelementaktivitäten aus Neutronenbestrahltem Selen mit Hilfe der Gegenstrom-Ionenwanderung

For the determination of trace elements in neutron irradiated, selenium by gamma-ray spectrometry the separation of the matrix activity is often necessary. In model experiments the decontamination of cation and anion impurities from the matrix solution was investigated by the counter current ion migration. After a processing of 3 hrs the trace activities of Co, Cr, Ga, Na and Zn were decontaminated from Se with a factor of >10³. For the trace elements As and Te representing the anionic constituents, a decontamination factor of 3·10² was obtained.     

Association of hydrofluoric acid in NaCl aqueous media under hydrothermal conditions

The apparent association constant of hydrofluoric acid Q _HF ^' in 1m NaCl aqueous media has been determined potentiometrically at pressures up to 1 kbar and temperatures up to 250°C. A concentration cell employing hydrogen electrodes was used. The association of HF increases with increasing temperature but decreases with increasing pressure.     

On the Sturm-Liouville operator

We consider the homogeneous Sturm-Liouville differential equation, prove the existence of two linearly independent solutions that form a fundamental system, and obtain some of their properties.     

How the Physicochemical Properties of the Bulk Material Affect the Ablation Crater Profile,Mass Balance,and Bubble Dynamics During Single-Pulse,Nanosecond Laser Ablation in Water

Understanding the key steps that drive the laser-based synthesis of colloids is a prerequisite for learning how to optimize the ablation process in terms of nanoparticle output and functional design of the nanomaterials. Even though many studies focus on cavitation bubble formation using single-pulse ablation conditions, the ablation efficiency and nanoparticle properties are typically investigated under prolonged ablation conditions with repetition rate lasers. Linking single-pulse and multiple-pulse ablation is difficult due to limitations induced by gas formation cross-effects, which occur on longer timescales and depend on the target materials’ oxidation-sensitivity. Therefore, this study investigates the ablation and cavitation bubble dynamics under nanosecond, single laser pulse conditions for six different bulk materials (Au, Ag, Cu, Fe, Ti, and Al). Also, the effective threshold fluences, ablation volumes, and penetration depths are quantified for these materials. The thermal and chemical properties of the corresponding bulk materials not only favor the formation of larger spot sizes but also lead to the highest molar ablation efficiencies for low melting materials such as aluminum. Furthermore, the concept of the cavitation bubble growth linked with the oxidation sensitivity of the ablated material is discussed. With this, evidence is provided that intensive chemical reactions occurring during the very early timescale of ablation are significantly enhanced by the bubble collapse.